For the paste specimen, the NRMSEs vary inversely with the collimator size when using a constant x-ray source intensity. As the collimator size decreases from collimator #3 to collimator #6, the NRMSEs increase from 1 % to 5 % (Fig. 4b). It is of interest to determine whether this variation in NRMSEs indicates that greater physical detail has been revealed (NRMSEs increase as the collimator size decreases) or that random noise due to x-ray beam intensity fluctuations or machine positioning errors from the measurements with the smaller collimators is greater (smaller collimators have fewer counts and so would have higher NRMSEs as discussed earlier). Tests were performed in which the counts were kept constant for each collimator by adjusting the x-ray source intensity, thereby eliminating the effect of counts on the NRMSEs. There is some indication that the NRMSEs for all collimators with constant counts follow the same pattern as with the variable counts, suggesting that the increase in paste NRMSEs for smaller collimators indicates greater detail in the profiles (the data for collimator #6 are the exception). However, the data are not conclusive.
Another way to determine whether or not increased NRMSEs indicate increased detail or are the result of random noise is to compute NRMSEs and NSD for a mean profile from several vertical scans. Machine positioning error would be averaged out when a sufficient number of scans were averaged together (assuming the errors are random) and the NRMSEs would approach zero. In this case, the NSD would indicate the amount of detail in the profile. Only one vertical profile was measured for the CVP experiments and so it is not possible to evaluate these statements for the CVP experiments at this time.
For the mortar specimen when using a constant x-ray source intensity, the largest collimators also result in the lowest NRMSE (Fig. 4c). However, the values for the smallest collimators (collimators #1, #5-7) are similar, in contrast to what was found for the paste and water specimens. This pattern for the mortar also exists when the number of counts is kept constant for each collimator, suggesting that random noise is not responsible for the pattern. As the collimator size decreases, the profiles become more detailed as indicated by the larger NRMSEs. With a vertical resolution of 1 mm, the profile data from collimators #2 and #3 (Table 2) are smoothed as some overlapping areas occur between adjacent points. For the smaller collimators, this smoothing does not exist. Moreover, the data from the smaller collimators show more small-scale variability due to a smaller field of view and the error in the positioning of the x-ray beam/detector that combine to maintain a high NRMSE.
When comparing the vertical profiles of the specimens that showed the lowest and highest NRMSE from the collimator experiments, the effect of the larger collimator size on reducing variability is clear. The paste and mortar profiles for collimator #2 show much less structure than the collimator #6 profiles (Figs. 5 and 6). So with a larger collimator, it is possible to reduce the amount of small-scale variability that is seen in the profiles, perhaps elucidating larger scale features of the specimen.The collimators are of known size and so it is possible to estimate the number of counts measured with a given collimator at a given intensity if the count data for just one of the collimators is available. The "Area Factor" is calculated by comparing the area of each collimator to the area of the largest collimator (collimator #2). For example, the Area Factor for collimator #3 is 2.9, which is determined by dividing the area of the largest collimator (9 mm2) by the area of collimator #3 (3.14 mm2; Table 2). If the counts for collimator #2 are divided by this Area Factor, an estimate of the number of counts for collimator #3 is obtained. For collimators #3-#7, the Area Factor determined from the water, paste, and mortar data is generally consistent with the machine specifications. The small differences between the expected Area Factor and the determined Area Factor perhaps result because the x-ray source intensity entering the collimator may not be uniform over the whole area due to a non-uniform x-ray source. The data for the water, paste, and mortar specimens provide an Area Factor of about 125 for collimator #1, while the machine specifications suggest that it should be 229. This data suggests that the dimensions of collimator #1 as provided are not correct and that the collimator is larger than specified.
Fig. 5. Normalized counts for the paste specimen in experiment CVP. The data were taken from vertical profiles with collimator #2 and collimator #6. See Table 1 for more information about experiment CVP and Table 2 for more information about the collimators.
Fig. 6. Normalized counts for the mortar specimen in experiment CVP. The data were taken from vertical profiles with collimator #2 and collimator #6. See Table 1 for more information about experiment CVP and Table 2 for more information about the collimators.